Our constructions only guarantee computational security, unlike the previous scheme of Broadbent and Lord. However, our assumptions are the best one can hope for: (a) a private-key uncloneable encryption scheme implies a post-quantum private encryption scheme (and thus, post-quantum one-way functions) and, (b) a public-key uncloneable encryption scheme implies a public-key encryption scheme. There are candidates from lattices for both post-quantum one-way functions and post-quantum public-key encryption schemes; for example, see [1]}.
